By comparing the flipper of the seal, sea-bear, and walrus with the fin and tail of the fish, whale, porpoise, etc.; and the wing of the penguin (a bird which is incapable of flight, and can only swim and dive) with the wing of the insect, bat, and bird, I have been able to show that a close analogy exists between the flippers, fins, and tails of sea mammals and fishes on the one hand, and the wings of insects, bats, and birds on the other; in fact, that theoretically and practically these organs, one and all, form flexible helices or screws, which, in virtue of their rapid reciprocating movements, operate upon the water and air by a wedge-action after the manner of twisted or double inclined planes. The twisted inclined planes act upon the air and water by means of curved surfaces, the curved surfaces reversing, reciprocating, and engendering a wave pressure, which can be continued indefinitely at the will of the animal. The wave pressure emanates in the one instance mainly from the tail of the fish, whale, porpoise, etc., and in the other from the wing of the insect, bat, or bird--_the reciprocating and opposite curves_ into which the tail and wing are thrown in swimming and flying constituting _the mobile helices, or screws_, which, during their action, produce the precise kind and degree of pressure adapted to fluid media, and to which they respond with the greatest readiness. In order to prove that sea mammals and fishes swim, and insects, bats, and birds fly, by the aid of curved figure-of-8 surfaces, which exert an intermittent wave pressure, I constructed artificial fish-tails, fins, flippers, and wings, which curve and taper in every direction, and which are flexible and elastic, particularly towards the tips and posterior margins. These artificial fish-tails, fins, flippers, and wings are slightly twisted upon themselves, and when applied to the water and air by a sculling or figure-of-8 motion, curiously enough reproduce the curved surfaces and movements peculiar to real fish-tails, fins, flippers, and wings, in swimming, and flying. Propellers formed on the fish-tail and wing model are, I find, the most effective that can be devised, whether for navigating the water or the air. To operate efficiently on fluid, _i.e._ yielding media, the propeller itself must yield. Of this I am fully satisfied from observation and experiment. The propellers at present employed in navigation are, in my opinion, faulty both in principle and application.